Eigenvectors and Eigenvalues
In a transformation, eigenvectors are the vectors that don't change direction, but get just scaled.
The factors by which they get scaled is called eigenvalue, and each eigenvactor has an associated eigenvalue.
There can also be no eigenvectors.
Example
Imagine we have two vectors in the basic plane:
We put the plane through the transformation:
Every other vector drifts to another direction, but not these guys.
These vectors just get scaled.
Info
The determinant of a matrix is the product of eigenvalues.
Info
In a 3D rotation, the axis of rotation is an eigenvector. It doesn't change direction.
Formal definition
The eigen vectors are such that when receiving a linear transformation, they stay on the same original direction, only scaled by their eigenvalue(